Distance Education Statistics Lab D Eric Parslow and Russell T. Hurlburt University of Nevada, Las Vegas

This lab will consist of 3 parts:
1. Practice using "mdist" in ESTAT.
2. Two exercises on the difference between a distribution of a variable and a distribution of means.
3. The Quiz.




PART 1

1. Open ESTAT and click on the tutorial labeled "mdist" (located on the right for Mac users / on the bottom left for Windows users)

2. Repeat the tutorial a few times using different sample sizes.

3. Your understanding of the difference between a distribution of a variable and a distribution of means should be solid. THIS IS CRITICAL TO SUCCESS IN THE REMAINDER OF THE COURSE.


PART 2 (you will need paper and pencil)

Problem 1:

Assume the cost of books at UNLV is normally distributed with a mean $50 and standard deviation $18.

a. Sketch the distribution. Don't forget to label the axis.

b. Shade the area on your distribution that refers to books that costover $41.

c. Eyeball-estimate the percentage of books over $41.


Answers:

a. Your axis should have been labeled 'Cost per book ($).' Your distribution should have been normal with a mean of $50 and labels at the tic marks indicating '-2, -1, 0, 1, and 2' standard deviations as '$14, $32, $50, $68, $86' respectively.

b. You should have shaded an area beginning at $41 and extending into the right-hand tail of the distribution.

c. Your estimate of books over $41 should have been 69% or 70%. Solution: The area between $41 and $50 is the large half of 34% (19% or 20%). The area beyond $50 is 50%. The total area is the sum of those two.

Continuing problem 1:

Assume that students buy 9 books per semester and that the cost of each book is a random sample from the population of UNLV book costs. You poll 100 students as to the cost of their books that semester and compute each student's mean cost per book.

d. Sketch the distribution of mean cost per book. Don't forget to label the axis.

e. Shade the area on your distribution that refers to an average of $41 or more per book.

f. Eyeball-estimate the percentage of students who pay an average of $41 or more per book?


Answers:

d. Your axis should have been labeled 'Mean cost per book ($), samples of size 9'. The distribution should be normal with mean of $50 and a standard error of $6 (18/sqr.rt. of 9 = 18/3 = 6). Your distribution should have had a mean of $50 and been labeled at the tic marks indicating '-2, -1, 0, 1, and 2' standard errors as '$38, $44, $50, $56, $62' respectively.

e. You should have shaded the area from $41 (1.5 standard errors below the mean) to the right-hand tail.

f. Your estimate of students paying more than an average of $41 should have been 93% or 94%. Solution: The area between $41 and $44 is the large half of 14% (9% or 10%); the area between $44 and $50 is 34%; and the area to the right of $50 is 50%. The total area is the sum of those three portions.


Problem 2:

Assume that basketball players' scores are normally distributed with mean 12 points per game and standard deviation 6 points

a. Sketch the distribution of players' points per game.

b. Shade the area on the distribution that refers to players who score over 18 points per game.

c. Eyeball-estimate the percentage of players who score over 18 points per game?


Answers:

a. The axis should be labeled 'Number of points per game.' Your distribution should have a mean of 12 and been labeled at the standard deviation tic marks '0, 6, 12, 18, 24'.

b. You should have shaded the area from 18 to the right-hand tail.

c. Your estimate of players scoring over 18 points per game should have been about 16%. Solution: There is 14% between 18 points and 24 points, and 2% above 24 points. The total area is the sum of those two portions.


Continuing problem 2:

Assume there are 9 players per team and 64 teams playing on a certain day. Suppose you select a team, ascertain the number of points each player scored, and compute the mean number of points scored by the players on that team. Then you select another team and compute the mean score for the 9 players on that team. Then you take another team, and another, until you have computed the mean score for the players on 64 teams.

d. Sketch what you would expect the distribution of mean points to look like.

e. Shade the area on the distribution of teams whose players average more than 18 points.

f. Eyeball-estimate the percentage of teams whose players average more than 18 points.


Answers:

d. The axis should be labeled 'Mean points scored, samples of size 9.' Your distribution should have a mean of 12 and a standard error of 2 (6/sqr.rt. of 9 = 6/3 = 2). Therefore your standard error tic marks should have been labeled '8, 10, 12, 14, 16' respectively.

e. You should have shaded the tiny region from 18 to the right-hand tail.

f. Your estimate of teams whose players average 18 points should have been very small -- under 1%. Solution: 18 points is 3 standard errors above the mean. The area beyond 3 standard errors is very small.

If you need further practice with these types of problems, refer to the exercises for Chapter 7 in the text or the Study Guide.



PART 3: THE QUIZ

Once you are comfortable with the distribution of variables, distributions of means, and their relationship, you are prepared to take the quiz.


You will need the quiz password, which is
7654321